Year: 2025
Type: article
Abstract: We investigate the components determining bigness of the cotangent bundle $$\Omega ^1_X$$ Ω X 1 of smooth models X in the birational class "Equation missing" of an orbifold surface of general type Y, with a focus on the contribution given by the singularities of Y. A criterion for bigness of $$\Omega _X^1$$ Ω X 1 is given involving only topological and singularity data on Y. We single out a special case, the Canonical Model Singularities (CMS) criterion, when Y is the canonical model of "Equation missing". We study the singularity invariants appearing in the criterion and determine them for $$A_n$$ A n singularities. Knowledge of these invariants for $$A_n$$ A n singularities allows one to evaluate the $$(c_2,c^2_1)$$ ( c 2 , c 1 2 ) -geographical range of the CMS criterion and compare it to other criteria. We obtain new examples of resolutions X of hypersurfaces $$Y\subset \mathbb {P}^3$$ Y ⊂ P 3 (with lower degrees) and of cyclic covers Y of $$\mathbb {P}^2$$ P 2 branched along line arrangements with $$\Omega ^1_X$$ Ω X 1 big.
Source: European Journal of Mathematics
Institution: University of Miami
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,490
OpenAlex ID: W4409312659